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I just have a quick confusion, so photoelectric effect says that light or photon act as particles not waves, however the photon energy is given by $E=hf$, so shouldn't the photon be initially a wave to start with because of frequency value?

I am so confused because it makes comparisons of what wave theory prediction would fail for photoelectric effect and hence particle theory is more appropriate but I just don't get the frequency value in calculating incoming photon energy to begin with. I would appreciate the clarification.

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The photoelectric effect expresses the fact that light behaves both as a wave and a particle. The fact that you use frequency to calculate the energy is obvious enough to you already that its wavelike property is demonstrated. The photoelectric effect however also reveals that energy is delivered by light in discrete amounts because regardless of the intensity of the light (the amount of light being delivered), electrons would not be excited until a certain frequency of light was reached. This suggested that the energy of light depended on its frequency.

Once the light did have enough energy by increasing the frequency of the light, increasing the intensity of the light increased the number of freed electrons proportionately - suggesting that a discrete quantized amount of energy was delivered to each electron. Light wasn't just some continuous flow of fluid, it was also independent amounts of energy that would manifest themselves via the number of freed electrons once the frequency was high enough.

This particle nature of light also explained why increasing the intensity of the light (the amount of light delivered to an electron) didn't excite the electron at frequencies below that magic value of frequency that excited an electron off the parent atom by exceeding its binding energy. It didn't matter if you sent more packets because the electron would interact with only one packet of light at a time; it mattered that the packet contained enough individual energy to free the electron.

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Snap a rope so that a wave begins to travel down it's length. The energy added is not the rope, but rather, inheres in the rope at the location where we see the wave. The electromagnetic field is like the rope which finds a quantum of energy (a photon) traversing across it and delivers this energy to a valence electron it may encounter. At this instant we can switch from our wave length description of energy to our classic particle description to describe the force required to break the valence bond. A quantum particle is not a particle when it is in transit and must encounter another particle (decelerate) to collapse the wave function since at that moment energies are reassigned. When we talk about 100 cubic feet per min. of air moving in a duct we don't expect to see actual cubic feet when we look inside the duct.

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